4" S&W .38 medium ("K") frame. Perhaps the most common/popular handgun ever made, for good reason. Flat out works. The Model 10 is the one that put the marque and format on the map for most folks. Subsequent "numbers" are basically different variations on the same theme.
A similar format Smith Model 65 .357 in holy grail 3" (IMO) or always "safe" 4", (but loaded usually with .38s or .38+Ps for the OP"sd purpose) - if you can find one within your budget.

Then add some nice comfy grips to help increase controllability and lessen felt recoil further - Hogue Monogrip/fingergroove - if you like soft "grippy" (somewhat sticky/tacky) feel--some do, some don't--or as I prefer Pachmayrs such as their Compac model - if less so.